Ratios (pages )

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1 A Ratios (pages 2 29) A ratio is a comparison of two numbers by division. Ratio Arithmetic: to : Algebra: a to b a:b a b When you write a ratio as a fraction, write it in simplest form. Two ratios that have the same value are equivalent ratios. You can also write ratios as decimals. 4, or A Alfredo gets a hit 2 out of every 0 times he goes to bat. Write this ratio as a fraction in simplest form. hits at bats The GCF of 2 and 0 is 2. Dan is 66 inches tall. Joaquin is 6 feet tall. Write the ratio of Dan s height to Joaquin s height in simplest form. 66 in. 6 ft 66 in. 72 in. Write both measurements in inches. 6 ft 72 in The GCF of 66 and 72 is 6. 2 Express each ratio as a fraction in simplest form. 2 HINT: Find the GCF and then simplify to 6 HINT: Write as a fraction. Find the GCF and simplify. Express each ratio as a fraction in simplest form. 6:9 4:. to 6. to 2 0:0 to 4 Tell whether the ratios are equivalent : and :2 0. 4:6 and 2: and 2. and 9 27 Standardized Test Practice Which of the following is tulips to 60 petunias written as a fraction in simplest form? 2 7 A C D Answers: yes 0. no. no 2. yes D Glencoe/McGraw-Hill Mathematics: Applications and Concepts, Course 2

2 A Rates (pages ) A rate is a ratio of two measurements with different units. A unit rate is a rate in which the denominator is unit. A In a bike race, Tariq rode 42 km in 2 hours. What was his unit rate? Write the rate as a fraction. Then find the equivalent rate with a denominator of. km hr The GCF of 42 and 2 is 2. 2 Tariq rode at a rate of 2 km per hour. Population density is the number of people per square mile. What is the population density of a town with a population of,20 and an area of square miles?,20 people sq. mi,20 Divide.,00 people per square mile Express each rate as a unit rate.. $0 for 0 days 2. revolutions in 2 minutes HINT: Write as a fraction. Then find the HINT: Write as a fraction. Then find the equivalent rate with a denominator of. equivalent rate with a denominator of. Express each rate as a unit rate. 00 tourists in 4 days 720 miles in days. 2 yards in minutes 6. $.9 for 2 ounces $22.2 for gallons 240 miles in hours 9. 6 books in 4 days 0. people in vans. Sales A company sold,000 popcorn poppers last year. On average, how many popcorn poppers did they sell each month? 2. Standardized Test Practice Which of the following gas stations sells gas for the best price per gallon? A $7 for gallons $6.64 for gallons C $26.00 for 20 gallons D $9.6 for 6 gallons Answers:. $ per day 2. 4 revolutions per minute 7 tourists per day 90 miles per day. 64 yards per minute 6. $0.99 per ounce $.24 per gallon 0 miles per hour 9. 4 books per day 0. 7 people per van. 20 popcorn poppers per month 2. D Glencoe/McGraw-Hill 6 Mathematics: Applications and Concepts, Course 2

3 A Solving Proportions (pages ) You can show that two ratios are equivalent with an equation called a proportion. When two ratios form a proportion, the cross products are equal. You can solve a proportion by using cross products to find a missing term. an you form a proportion with the ratios and? Set the ratios equal to each other and 2 0 Since the cross products are equal, the ratios form a proportion. u 64 6 u 6 64 Find the cross products. 6u 92 Solve. 6u Divide each side by 6. u 2 The solution is 2. Solve each proportion. 2 x 9 Hint: 2 9 x.. 2. y 4 Hint: Find the cross products. Solve each proportion z 40 n 0 j f p q 2 r 6 k 0 x. Find the value of x that makes a proportion. 2. Surveys A survey at Lincoln Middle School found that 6 of every 0 students prefer math class to science class. If there are 400 students at the school, how many of them would you expect to prefer math class to science class? 20 Standardized Test Practice A factory can produce,00 cans of juice in hours. How many cans of juice can they produce in hours? A 2,000 4,000 C,000 D 6,000 Answers: Glencoe/McGraw-Hill 7 Mathematics: Applications and Concepts, Course 2

4 A Scale Drawings (pages 04 0) You can use a scale drawing to represent something that is too large or too small for an actual-size drawing. A map is an example of a scale drawing. The scale on a map is the ratio of the distance on the map to the actual distance. A Tracy and Tyrone are planning a hiking trip. On the map, their route is cm long. The map scale says that cm represents km. What is the actual length of their hike? Let d represent the hiking distance. Write and solve a proportion. map distance actual distance cm km cm d d d 22. The actual length is 22. km. The scale of a blueprint is in. 4 ft. If the actual width of a porch is 6 ft, what is the width on the blueprint? Let w represent the porch width. Write and solve a proportion. blueprint width actual width in. 4 ft 6 4 w 6 4w w The width on the blueprint is 4 inches. w 6 ft 4w 4 Find the length of each object on a scale drawing with the given scale.. a house 7 feet long; inch: foot 2. a box meters tall; cm:. m Find the length of each object on a scale drawing with the given scale. a desk meters long; 2 centimeters: meter an airplane with a 4-meter wingspan; centimeters: meter. an automobile that is feet wide; 0. inch: foot 6. a street that is 2 miles long; inches: mile Find how far it is across the city of loomington if it is 2.4 centimeters on a map that has a scale of centimeter: kilometers. Architecture The Sears Tower in downtown Chicago is 0 stories high. A scale drawing has a scale of. centimeters: story. How tall is the Sears Tower on the scale drawing? 9. Standardized Test Practice Which is the actual length of a sofa that is 4 inches on a scale drawing if the scale is 2 inches: feet? A 0 feet 20 feet C feet D 0 feet Answers:. 7 in cm 9 cm 62 cm. 4 in in. km 6 cm 9. A Glencoe/McGraw-Hill Mathematics: Applications and Concepts, Course 2

5 A Fractions, Decimals, and Percents (pages 2 ) You can use a proportion to express a fraction as a percent. To write a percent as a fraction, begin with a fraction that has a denominator of 00. Then write the fraction in simplest form. Recall that n%. n 00 A Write as a percent. Write a proportion 400 n Multiply to find the cross products n Divide each side by. 0 n n 00 0% Write 24% as a fraction in simplest form. Estimate: 24% is about 2%, which is % The GCF is % 2 Compare to the estimate. Write each fraction as a percent n HINT: Solve a proportion in which the fraction is equal to 00. Write each fraction as a percent Write each percent as a fraction is simplest form % 0. %. 2% % % 0%. % 6. % Hobbies At a hot air balloon festival, 60% of the hot air balloons were partially colored red. Write the percent of hot air balloons that were partially colored red as a fraction in simplest form. Standardized Test Practice A store advertised a sale where every item was off. What is this fraction written as a percent? A 2.% 2.% C 22.% D % Answers:. 40% 2. 0% 0% 7%. % 6. 7% 2% 60% Glencoe/McGraw-Hill 9 Mathematics: Applications and Concepts, Course 2

6 A Percents Greater Than 00% and Percents Less Than % (pages 6 ) When you express a percent greater than 00% as a decimal, the resulting decimal is greater than. When you express a percent less than % as a decimal, the resulting decimal is less than 0.0. A Write 42% as a decimal. Write as a percent. 42%.42 Divide the percent by 00 and % Multiply the decimal by remove the percent symbol. 00 and add the percent symbol.. Express 0.62% as a decimal. 2. Express 7 as a percent. HINT: The resulting decimal is less than 0.0. HINT: The decimal is greater than. Express each percent as a decimal. 2% 4%. 20% 6. 6% 0.0% 0.% Express each number as a percent ,000. Write 40% as a decimal. 6. Express as a percent. Internet Lara and Lezlie both use the Internet. Lara s Internet usage is 60% of Lezlie s. y what decimal would you multiply Lezlie s usage to get Lara s usage? Standardized Test Practice The area of Indiana is about of the area of the United states. What is written as a percent? A 0.9% 9% C 9.% D 0.009% Answers: % % %. 2% 2. 40% 6% 0.4% %.6 A Glencoe/McGraw-Hill 60 Mathematics: Applications and Concepts, Course 2

7 A Percent of a Number (pages 9 2) Suppose you read in the school newspaper that 62% of students who were surveyed buy their lunches at school. Of the 200 students who were surveyed, how many buy their lunches? You can either use a proportion or multiplication to solve this problem. A Find 62% of 200. Method : Use a proportion. Let s represent the number of students who buy their lunches. s The ratio of s students to the 200 who were surveyed equals 62%, 62 or 00. s Find the cross products. 00s 2, Divide each side by 00. s 24 So, 62% of 200 is 2 Find 62% of 200. Method 2: Use multiplication. First express the percent as a decimal and then multiply. 62% of Remember, 62% So, 62% of 200 is 2 Find each number. Round to the nearest tenth if necessary.. Find 0% of What number is 20% of 200? Find each number. Round to the nearest tenth if necessary. Find 0% of 40. What number is 7% of 24?. What number is 2% of 6? 6. % of 22 is what number? Find 2% of 60. Find % of % of 74 is what number? 0. What number is 7% of 2?. What number is % of 96? 2. Find 0% of 00. Landscaping Mr. and Mrs. Morrisey want to replace 60% of the grass in their yard with bushes and plants. If their yard has 6,000 square feet of grass, how many square feet will be replaced with bushes and plants? Standardized Test Practice If 2% of the pieces of a 00-piece puzzle are edge pieces, how many are edge pieces? A 7 0 C 2 D 22 Answers: ,600 C Glencoe/McGraw-Hill 6 Mathematics: Applications and Concepts, Course 2

8 A The Percent Proportion (pages 2 2) a p The percent proportion is, where a represents the part, b 00 b represents the base, and p represents the percent. Using the proportion , you can see how to use the percent proportion to solve the three basic types of percent equations. Find the Percent is what percent of 2? Find the Part What number is 0% of 2? Find the ase is 0% of what number? 0 b 00 2 a 2 p A 2 is 40% of what number? 2 b Write the percent proportion replacing a with 2 and p with b 40 Find the cross products.,200 40b Divide each side by b So, 2 is 40% of 0. 0 is what percent of 0? Write the percent proportion replacing a with 0 and b with p Find the cross products.,000 0p 0 0 Divide each side by p So, 0 is 20% of 0. Find each number. Round to the nearest tenth if necessary.. 6 is what percent of 2? 2. What number is 6% of 90? 0 0 p 00 Find each number. Round to the nearest tenth if necessary. What percent of 24 is 6? What percent of 40 is?. % of what number is 0? 6. is 0% of what number? What number is 60% of 20? What percent of 96 is 2? 9. What percent of 400 is 60? 0. What number is 2% of 0?. Find 0% of is 4% of what number? Standardized Test Practice During a flu epidemic, of the 20 students in Marina s class were absent with the flu. What percent of the students in Marina s class were absent? A 0% % C 20% D % Answers:. 0% % 20% % 9. % D Glencoe/McGraw-Hill 62 Mathematics: Applications and Concepts, Course 2

9 Chapter 7 Review Commercial Percents Television stations and networks sell advertising time, called commercials, to pay for the cost of running the station and network, and to pay for producing the programs that you watch. Have you ever wondered how much time you spend watching commercials instead of programs? With a parent, follow the steps below to find out. Note: If you or your parent would rather not watch television, you can complete this same exercise by listening to the radio.. Decide on a television program to watch. efore the program starts, have this worksheet, a pencil, and a watch with a second hand ready. 2. Using the table below, record the exact time the program begins. Then, using the watch, record the length of time of every commercial break during the program. Networks and television stations usually show four or more commercials in a row, so be sure to record the length of time of each entire commercial break. Also be sure to record the length of time of the commercials after the program, right up until the next program begins. Once you have watched the entire program, find the percent of time you spent watching commercials and the percent of time you spent watching the program. Use the table below to help you. Program Start Time Program End Time Total Program Time (minutes) Commercial reaks reak reak 2 reak reak 4 reak (add more breaks if you need them) Total Time of Commercials (minutes) Time Use the percent proportion to find out what percent of the program s time was spent on commercials. The total time (in minutes) of the commercials is the percentage (P) and the total program time is the base (). You are looking for r. Round your result to the nearest whole percent. P r 00 Percentage of time for commercials: Try this activity with different kinds of programs, with programs of different lengths, and with programs shown at different times of the day. Are the percentages the same? Explain. Answers are located on page 0 Glencoe/McGraw-Hill 6 Mathematics: Applications and Concepts, Course 2